Domino's Pizza Pricing: Cost Per Topping
My family loves to eat Domino’s pizza (and we’ve been eating a lot more of it since this program started). However, I’ve always been curious about the price we pay for pizza – especially the cost per topping. Unfortunately Domino’s isn’t very transparent with their pricing. They don’t tell you how much the toppings cost; they only tell you the final price of your pizza after you build it.
So for my mathematizing project, I decided to analyze the cost per topping of Domino’s pizza. I’ve looked at a variety of different scenarios which are detailed below (note: all pricing is for take-out pizza):
Scenario 1: Cost per Non-meat Topping
In this scenario, I tried to calculate the cost per non-meat topping since my family is vegetarian. I used Domino’s online website to build a Medium (12") Hand Tossed Pizza with two toppings: Black Olives, Green Peppers. Then I built another pizza, a Medium (12") Hand Tossed Pizza with four toppings: Black Olives, Green Peppers, Mushrooms, and Diced Tomatoes. I was able to calculate the cost per topping by comparing the prices of the two pizzas:
Then I tried to assess whether the pricing is linear – that is, is the cost per topping constant as the number of toppings increases? The pricing is indeed linear and after graphing the data, I was able to calculate the trend line: y = 1.59x + 10.40. Given the linear model, I would expect the base price of a Medium (12") Hand Tossed Pizza without toppings to be $10.40. However, it wasn’t. It was actually $11.99 – the same price as a single topping pizza. So for all you pizza lover’s out there, you might as well order one topping for your pizza since you are really paying for it anyway. In addition, Domino’s only lets you order 10 toppings so the value for x can’t be any greater than 10 in the linear model. Here are my results:
Scenario 2:Cost per Meat Topping
Next I tried to determine whether meat toppings cost more than non-meat toppings. Since meat usually costs more than vegetables, I would expect the price per meat topping to cost more. I used Domino’s online website to build a variety of pizzas with meat toppings. From the trend line on the graph below, you can see that the price per topping is the same for meat toppings as it is for non-meat toppings. There are only 9 meat toppings to choose from vs. 10+ non-meat toppings. So now I know the price per topping is really the same across all different toppings – meat does not cost more.
Here are the results:
Scenario 3: Cost per Topping – Different Pizza Sizes For this scenario, I tried to determine whether Domino’s charges more per topping depending on the size of the pizza. I would expect the cost per topping to be less on a small pizza than a large pizza because a large pizza can fit a greater amount of toppings. My results matched my prediction since the cost per topping for a small pizza is $1.29 and the cost per topping for a large pizza is $1.79. As an extension to this activity, I calculated the cost per square inch to see if there were any economies of scale (i.e. is there a reduction in per unit cost as the volume increases). Using the area formula for a circle A=πr^2 I determined the total area for each different pizza size. Then I divided the cost per topping for that pizza size by the area to arrive at the cost per square inch of pizza. My results confirmed that there are economies of scale since the cost per square inch is smaller for a large pizza than for a small pizza.
Here are the results:
Scenario 4:Domino's vs. Papa John'sCost per Topping
In this scenario I tried to determine whether Papa John's charges more per topping than Domino's. Since Papa John's uses much more descriptive language when describing its toppings, the price per topping sounds more expensive. I used Papa John's online website to build a Medium (12") Hand Tossed Pizza with two toppings: Black Olives, Green Peppers. Then I built another pizza, a Medium (12") Hand Tossed Pizza with four toppings: Black Olives, Green Peppers, Mushrooms, and Diced Tomatoes. I was able to calculate the cost per topping by comparing the prices of the two pizzas. Even though the overall price of a Papa John's pizza is more expensive than a Domino's Pizza, the price per topping is exactly the same. Here are the results: The Mathematics Supporting this Exploration:
This lesson is targeted at 8th grade students. In this lesson students will use linear equations to
understand Domino's pizza pricing model. Since pizza is a well known, favorite food of many middle schools students, they should enjoy using it in this lesson to explore mathematical concepts. Here is an overview of the lesson objectives: Students will
Understand the ideas of slope and y-intercept within the context of Domino’s pizza pricing
Write and graph a linear equation given two (or more) points on the line
Understand what it means for a function to be linear (constant rate of change)
The objectives relate to the following Common Core Standards for 8th grade Mathematics: CCSS.Math.Content.8.EE.B.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. CCSS.Math.Content.8.F.A.3 Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. CCSS.Math.Content.8.F.B.4 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. CCSS.Math.Content.8.F.B.5 Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.
Potential Extensions:
Domino's allows you to put different quantities of each topping on their pizzas: Light, Normal, Extra, Double, Triple. It might be interesting to see what the price per topping is for these different quantities - I.e. does Domino's really charge twice the amount per topping for a double serving?
It might be interesting to look at other variables that drive Domino's pizza pricing - for example different crust types, delivery vs. take-out, etc.
There may be other pizza chains that use a different pricing scheme. It might be interesting to examine their pricing structure.
Domino's Pizza Pricing: Cost Per Topping
My family loves to eat Domino’s pizza (and we’ve been eating a lot more of it since this program started). However, I’ve always been curious about the price we pay for pizza – especially the cost per topping. Unfortunately Domino’s isn’t very transparent with their pricing. They don’t tell you how much the toppings cost; they only tell you the final price of your pizza after you build it.
So for my mathematizing project, I decided to analyze the cost per topping of Domino’s pizza. I’ve looked at a variety of different scenarios which are detailed below (note: all pricing is for take-out pizza):
Scenario 1: Cost per Non-meat Topping
In this scenario, I tried to calculate the cost per non-meat topping since my family is vegetarian. I used Domino’s online website to build a Medium (12") Hand Tossed Pizza with two toppings: Black Olives, Green Peppers. Then I built another pizza, a Medium (12") Hand Tossed Pizza with four toppings: Black Olives, Green Peppers, Mushrooms, and Diced Tomatoes. I was able to calculate the cost per topping by comparing the prices of the two pizzas:
Then I tried to assess whether the pricing is linear – that is, is the cost per topping constant as the number of toppings increases? The pricing is indeed linear and after graphing the data, I was able to calculate the trend line: y = 1.59x + 10.40. Given the linear model, I would expect the base price of a Medium (12") Hand Tossed Pizza without toppings to be $10.40. However, it wasn’t. It was actually $11.99 – the same price as a single topping pizza. So for all you pizza lover’s out there, you might as well order one topping for your pizza since you are really paying for it anyway. In addition, Domino’s only lets you order 10 toppings so the value for x can’t be any greater than 10 in the linear model. Here are my results:
Next I tried to determine whether meat toppings cost more than non-meat toppings. Since meat usually costs more than vegetables, I would expect the price per meat topping to cost more. I used Domino’s online website to build a variety of pizzas with meat toppings. From the trend line on the graph below, you can see that the price per topping is the same for meat toppings as it is for non-meat toppings. There are only 9 meat toppings to choose from vs. 10+ non-meat toppings. So now I know the price per topping is really the same across all different toppings – meat does not cost more.
Here are the results:
For this scenario, I tried to determine whether Domino’s charges more per topping depending on the size of the pizza. I would expect the cost per topping to be less on a small pizza than a large pizza because a large pizza can fit a greater amount of toppings. My results matched my prediction since the cost per topping for a small pizza is $1.29 and the cost per topping for a large pizza is $1.79. As an extension to this activity, I calculated the cost per square inch to see if there were any economies of scale (i.e. is there a reduction in per unit cost as the volume increases). Using the area formula for a circle A=πr^2 I determined the total area for each different pizza size. Then I divided the cost per topping for that pizza size by the area to arrive at the cost per square inch of pizza. My results confirmed that there are economies of scale since the cost per square inch is smaller for a large pizza than for a small pizza.
Here are the results:
Scenario 4: Domino's vs. Papa John's Cost per Topping
In this scenario I tried to determine whether Papa John's charges more per topping than Domino's. Since Papa John's uses much more descriptive language when describing its toppings, the price per topping sounds more expensive. I used Papa John's online website to build a Medium (12") Hand Tossed Pizza with two toppings: Black Olives, Green Peppers. Then I built another pizza, a Medium (12") Hand Tossed Pizza with four toppings: Black Olives, Green Peppers, Mushrooms, and Diced Tomatoes. I was able to calculate the cost per topping by comparing the prices of the two pizzas. Even though the overall price of a Papa John's pizza is more expensive than a Domino's Pizza, the price per topping is exactly the same. Here are the results:
The Mathematics Supporting this Exploration:
This lesson is targeted at 8th grade students. In this lesson students will use linear equations to
understand Domino's pizza pricing model. Since pizza is a well known, favorite food of many middle schools students, they should enjoy using it in this lesson to explore mathematical concepts. Here is an overview of the lesson objectives:
Students will
The objectives relate to the following Common Core Standards for 8th grade Mathematics:
CCSS.Math.Content.8.EE.B.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.
CCSS.Math.Content.8.F.A.3 Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear.
CCSS.Math.Content.8.F.B.4 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
CCSS.Math.Content.8.F.B.5 Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.
Potential Extensions:
References:
This lesson was adapted from the following lesson at the Mathalicious website: http://www.mathalicious.com/lessons/domino-effect